Fig. 2: Angular momentum dispersion. | Nature Communications

Fig. 2: Angular momentum dispersion.

From: Simulating hyperbolic space on a circuit board

Fig. 2

a Rescaled frequency \({\lambda }_{{{{{{{{\rm{g}}}}}}}}}^{n\ell }\) vs. angular momentum for eigenmodes \({u}_{{{{{{{{\rm{g}}}}}}}}}^{n\ell }\) of the continuum Laplace-Beltrami operator, i.e., solutions to Eq. (2), for the Euclidean (left) and hyperbolic (right) geometry. For the first six branches, the value of n is indicated by red numbers. b Same data for a Euclidean {3, 6} (left) and hyperbolic {3, 7} (right) tessellation, each with 85 sites. For the hyperbolic lattice, we additionally show the experimental results (orange squares) obtained from the electric circuit.

Back to article page